Compressor blade for a gas turbine engine

ABSTRACT

An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

RELATED APPLICATIONS

The present application is related to U.S. Pat. No. 15/208,047 AND 15/208,089 filed concurrently herewith, which are each fully incorporated by reference herein and made a part hereof.

BACKGROUND OF THE INVENTION

The present invention relates generally to an airfoil for use in turbomachinery, and more particularly relates to an airfoil profile or airfoil shape for use in a compressor.

In turbomachines, many system requirements should be met at each stage of the turbomachine's flow path to meet design goals. These design goals include, but are not limited to, overall improved efficiency, reduction of vibratory response and improved airfoil loading capability. For example, a compressor airfoil profile should achieve thermal and mechanical operating requirements for a particular stage in the compressor. Moreover, component lifetime, reliability and cost targets also should be met.

BRIEF DESCRIPTION OF THE INVENTION

According to one aspect of the present invention an article of manufacture is provided having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

According to another aspect of the present invention an article of manufacture is provided having a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z coordinate values being scalable as a function of the number to provide one of a non-scaled, scaled-up and scaled-down airfoil profile.

According to yet another aspect of the present invention a compressor is provided comprising a plurality of rotor blades, each of the rotor blades including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape.

These and other features and improvements of the present invention should become apparent to one of ordinary skill in the art upon review of the following detailed description when taken in conjunction with the several drawings and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a compressor flow path through multiple stages and illustrates exemplary compressor stages according to an aspect of the invention;

FIG. 2 is a perspective view of a rotor blade, according to an aspect of the invention; and

FIG. 3 is a cross-sectional view of the rotor blade airfoil taken generally about line 3-3 in FIG. 2, according to an aspect of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

One or more specific aspects/embodiments of the present invention will be described below. In an effort to provide a concise description of these aspects/embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with machine-related, system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the present invention, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Any examples of operating parameters and/or environmental conditions are not exclusive of other parameters/conditions of the disclosed embodiments. Additionally, it should be understood that references to “one embodiment”, “one aspect” or “an embodiment” or “an aspect” of the present invention are not intended to be interpreted as excluding the existence of additional embodiments or aspects that also incorporate the recited features. Turbomachinery is defined as one or more machines that transfer energy between a rotor and a fluid or vice-versa, including but not limited to gas turbines, steam turbines and compressors.

Referring now to the drawings, FIG. 1 illustrates an axial compressor flow path 1 of a compressor 2 that includes a plurality of compressor stages. The compressor 2 may be used in conjunction with, or as part of, a gas turbine. As one non-limiting example only, the compressor flow path 1 may comprise about eighteen rotor/stator stages. However, the exact number of rotor and stator stages is a choice of engineering design, and may be more or less than the illustrated eighteen stages. It is to be understood that any number of rotor and stator stages can be provided in the compressor, as embodied by the invention. The eighteen stages are merely exemplary of one turbine/compressor design, and are not intended to limit the invention in any manner.

The compressor rotor blades 22 impart kinetic energy to the airflow and therefore bring about a desired pressure rise. Directly following the rotor blades 22 is a stage of stator compressor vanes 23. However, in some designs the stator vanes may precede the rotor blades. Both the rotor blades and stator vanes turn the airflow, slow the airflow velocity (in the respective airfoil frame of reference), and yield a rise in the static pressure of the airflow. Typically, multiple rows of rotor/stator stages are arranged in axial flow compressors to achieve a desired discharge to inlet pressure ratio. Each rotor blade and stator vane includes an airfoil, and these airfoils can be secured to rotor wheels or a stator case by an appropriate attachment configuration, often known as a “root,” “base” or “dovetail”. In addition, compressors may also include inlet guide vanes (IGVs) 21, variable stator vanes (VSVs) 25 and exit or exhaust guide vanes (EGVs) 27. All of these blades and vanes have airfoils that act on the medium (e.g., air) passing through the compressor flow path 1.

Exemplary stages of the compressor 2 are illustrated in FIG. 1. One stage of the compressor 2 comprises a plurality of circumferentially spaced rotor blades 22 mounted on a rotor wheel 51 and a plurality of circumferentially spaced stator vanes 23 attached to a static compressor case 59. Each of the rotor wheels 51 may be attached to an aft drive shaft 58, which may be connected to the turbine section of the engine. The rotor blades and stator vanes lie in the flow path 1 of the compressor 2. The direction of airflow through the compressor flow path 1, as embodied by the invention, is indicated by the arrow 60 (FIG. 1), and flows generally from left to right in the illustration.

The rotor blades 22 and stator vanes 23 herein of the compressor 2 are merely exemplary of the stages of the compressor 2 within the scope of the invention. In addition, each inlet guide vane 21, rotor blade 22, stator vane 23, variable stator vane 25 and exit guide vane 27 may be considered an article of manufacture. Further, the article of manufacture may comprise a rotor blade configured for use with a compressor.

A rotor blade 22, illustrated in FIG. 2, is provided with an airfoil 200. Each of the rotor blades 22 has an airfoil profile at any cross-section from the airfoil root 220 to the airfoil tip 210. The airfoil connects to a mounting base 260, which may also be referred to as a dovetail. The mounting base fits into a complementary shaped groove or slot in the rotor or rotor wheel 51.

Embodiments of the compressor may incorporate a variety of blades 22 and vanes 21, 23, 25, 27 arranged in multiple stages.

Referring to FIG. 3, it will be appreciated that each rotor blade 22 has an airfoil 200 as illustrated. The airfoil 200 has a suction side 310 and a pressure side 320. The suction side 310 is located on the opposing side of the airfoil from the pressure side 320. Thus, each rotor blade 22 has an airfoil profile at any cross-section in the shape of the airfoil 200. The airfoil 200 also includes a leading edge 330 and a trailing edge 340, and a chord length 350 extends therebetween. The root of the airfoil corresponds to the lowest non-dimensional Z value of scalable Table 1. The tip of the airfoil corresponds to the highest non-dimensional Z value of scalable Table 1. An airfoil may extend beyond the compressor flowpath and may be tipped to achieve the desired endwall clearances. As non-limiting examples only, the height of the airfoil 200 may be from about 1 inch to about 20 inches or more, about 2 inches to about 18 inches, or about 4 inches to about 15 inches. However, any specific airfoil height may be used as desired in the specific application.

The compressor flow path 1 requires airfoils that meet system requirements of aerodynamic and mechanical blade/vane loading and efficiency. For example, it is desirable that the airfoils are designed to reduce the vibratory response or vibratory stress response of the respective blades and/or vanes. Materials such as high strength alloys, non-corrosive alloys and/or stainless steels may be used in the blades and/or vanes. To define the airfoil shape of each blade airfoil and/or vane airfoil, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. These unique loci of points meet the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine and compressor to run in an efficient, safe, reliable and smooth manner. These points are unique and specific to the system. The locus that defines the airfoil profile includes a set of points with X, Y and Z coordinates relative to a reference origin coordinate system. The three-dimensional Cartesian coordinate system of X, Y and Z values given in scalable Table 1 below defines the profile of the rotor blade airfoil at various locations along its length. Scalable Table 1 list data for a non-coated airfoil. The envelope/tolerance for the coordinates is about +/−5% of the chord length 350 in a direction normal to any airfoil surface location, or about +/−0.25 inches in a direction normal to any airfoil surface location. However, tolerances of about +/−0.15 inches to about +/−0.25 inches, or about +/−3% to about +/−5% in a direction normal to an airfoil surface location may also be used, as desired in the specific application.

The point data origin 230 may be the mid-point of the suction or pressure side of the base of the airfoil, the leading edge or trailing edge of the base of the airfoil, or any other suitable location as desired. The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units in scalable Table 1, although other units of dimensions may be used when the values are appropriately converted. As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a multiplying by a constant number (e.g., 100). The number, used to convert the non-dimensional values to dimensional distances, may be a fraction (e.g., ½, ¼, etc.), decimal fraction (e.g., 0.5, 1.5, 10.25, etc.), integer (e.g., 1, 2, 10, 100, etc.) or a mixed number (e.g., 1½, 10¼, etc.). The dimensional distances may be any suitable format (e.g., inches, feet, millimeters, centimeters, meters, etc.). As one non-limiting example only, the Cartesian coordinate system has orthogonally-related X, Y and Z axes and the X axis may lie generally parallel to the compressor rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward the aft, i.e., exhaust end of the turbine. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the rotor blade tip or stator vane base. All the values in scalable Table 1 are given at room temperature and are unfilleted.

By defining X and Y coordinate values at selected locations in a Z direction (or height) normal to the X, Y plane, the profile section or airfoil shape of the airfoil, at each Z height along the length of the airfoil can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each Z height is fixed. The airfoil profiles of the various surface locations between each Z height are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The values in Table 1 are generated and shown from zero to four or more decimal places for determining the profile of the airfoil. As the airfoil heats up the associated stress and temperature will cause a change in the X, Y and Z values. Accordingly, the values for the profile given in Table 1 represent ambient, non-operating or non-hot conditions (e.g., room temperature) and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as optional coatings which must be accounted for in the actual profile of the airfoil. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in Table 1 below. Accordingly, a distance of about +/−5% of chord length and/or +/−0.25 inches in a direction normal to a surface location along the airfoil profile defines an airfoil profile envelope for this particular airfoil design and compressor, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the Tables below at the same temperature. Additionally, a distance of about +/−5% of a chord length in a direction normal to an airfoil surface location along the airfoil profile also may define an airfoil profile envelope for this particular airfoil design. The data is scalable and the geometry pertains to all aerodynamic scales, at, above and/or below about 3,600 RPM. The rotor blade airfoil design is robust to this range of variation without impairment of mechanical and aerodynamic functions.

The coordinate values given in scalable Table 1 below provide the nominal profile for exemplary stages of a compressor rotor blade.

TABLE 1 SUCTION SIDE PRESSURE SIDE X Y Z X Y Z 3.5567 0.6761 −0.25 −3.4823 0.5026 −0.25 3.5595 0.6647 −0.25 −3.4818 0.504 −0.25 3.5617 0.6494 −0.25 −3.4805 0.5066 −0.25 3.5619 0.6299 −0.25 −3.478 0.5118 −0.25 3.5585 0.6069 −0.25 −3.4728 0.5222 −0.25 3.5478 0.5776 −0.25 −3.4633 0.5376 −0.25 3.5246 0.5447 −0.25 −3.4428 0.563 −0.25 3.4836 0.5155 −0.25 −3.4105 0.5917 −0.25 3.4287 0.4875 −0.25 −3.3608 0.6211 −0.25 3.3633 0.4541 −0.25 −3.2927 0.6443 −0.25 3.2868 0.4151 −0.25 −3.2003 0.6549 −0.25 3.1963 0.3693 −0.25 −3.0929 0.6462 −0.25 3.0916 0.3167 −0.25 −2.9805 0.6234 −0.25 2.9727 0.2578 −0.25 −2.8549 0.5933 −0.25 2.8394 0.1928 −0.25 −2.7152 0.5608 −0.25 2.6915 0.1222 −0.25 −2.5611 0.5278 −0.25 2.5287 0.0464 −0.25 −2.3994 0.4959 −0.25 2.358 −0.0305 −0.25 −2.2302 0.4658 −0.25 2.1791 −0.1079 −0.25 −2.0532 0.4387 −0.25 1.9917 −0.1853 −0.25 −1.8682 0.4159 −0.25 1.7956 −0.2618 −0.25 −1.6752 0.3981 −0.25 1.5903 −0.3365 −0.25 −1.4746 0.3852 −0.25 1.3756 −0.4085 −0.25 −1.2665 0.3773 −0.25 1.1517 −0.4766 −0.25 −1.0511 0.3749 −0.25 0.9259 −0.5376 −0.25 −0.8356 0.3779 −0.25 0.6981 −0.5912 −0.25 −0.6204 0.386 −0.25 0.4684 −0.6368 −0.25 −0.4053 0.3983 −0.25 0.2372 −0.6739 −0.25 −0.1904 0.4141 −0.25 0.0051 −0.7016 −0.25 0.0242 0.4325 −0.25 −0.2281 −0.7192 −0.25 0.2388 0.4526 −0.25 −0.4623 −0.726 −0.25 0.4531 0.474 −0.25 −0.6963 −0.7212 −0.25 0.6675 0.496 −0.25 −0.9295 −0.7043 −0.25 0.8818 0.5183 −0.25 −1.1619 −0.6754 −0.25 1.096 0.5408 −0.25 −1.3923 −0.6353 −0.25 1.3103 0.5632 −0.25 −1.6119 −0.5866 −0.25 1.5175 0.5847 −0.25 −1.8211 −0.5306 −0.25 1.7175 0.6052 −0.25 −2.0204 −0.4683 −0.25 1.9104 0.6248 −0.25 −2.2101 −0.4012 −0.25 2.0962 0.6435 −0.25 −2.3906 −0.3302 −0.25 2.2749 0.6613 −0.25 −2.5622 −0.2567 −0.25 2.4464 0.6782 −0.25 −2.7251 −0.1817 −0.25 2.6108 0.6942 −0.25 −2.879 −0.106 −0.25 2.7609 0.7088 −0.25 −3.0162 −0.032 −0.25 2.8967 0.722 −0.25 −3.136 0.0414 −0.25 3.0183 0.7337 −0.25 −3.2375 0.1139 −0.25 3.1255 0.7441 −0.25 −3.3269 0.1894 −0.25 3.2184 0.7531 −0.25 −3.3973 0.2627 −0.25 3.297 0.7607 −0.25 −3.4439 0.3254 −0.25 3.3642 0.7672 −0.25 −3.4733 0.3803 −0.25 3.4207 0.7726 −0.25 −3.4877 0.4251 −0.25 3.467 0.7672 −0.25 −3.4911 0.4603 −0.25 3.5014 0.7512 −0.25 −3.4891 0.4798 −0.25 3.5239 0.7326 −0.25 −3.4858 0.4921 −0.25 3.5379 0.7156 −0.25 −3.4839 0.4981 −0.25 3.5473 0.6999 −0.25 −3.4829 0.5011 −0.25 3.5532 0.6866 −0.25 3.5545 0.5874 0 −3.4655 0.5312 0 3.5571 0.5761 0 −3.4649 0.5326 0 3.5588 0.5608 0 −3.4637 0.5352 0 3.5583 0.5415 0 −3.4612 0.5404 0 3.5537 0.5189 0 −3.4559 0.5507 0 3.5413 0.4907 0 −3.4461 0.5659 0 3.5154 0.4601 0 −3.4247 0.5905 0 3.4722 0.435 0 −3.3909 0.6173 0 3.4172 0.4082 0 −3.3395 0.6429 0 3.3518 0.3764 0 −3.2699 0.6606 0 3.2752 0.3392 0 −3.177 0.6645 0 3.1846 0.2956 0 −3.0704 0.6512 0 3.0798 0.2457 0 −2.9584 0.628 0 2.9606 0.1899 0 −2.833 0.5996 0 2.8271 0.1284 0 −2.6934 0.5688 0 2.6789 0.0617 0 −2.5394 0.5373 0 2.5159 −0.0097 0 −2.378 0.5067 0 2.345 −0.0821 0 −2.2092 0.4775 0 2.166 −0.1548 0 −2.033 0.4508 0 1.9786 −0.2272 0 −1.849 0.4275 0 1.7826 −0.2987 0 −1.6573 0.4081 0 1.5776 −0.3684 0 −1.4579 0.3928 0 1.3633 −0.4353 0 −1.2509 0.3817 0 1.1399 −0.4982 0 −1.0367 0.3753 0 0.9149 −0.5542 0 −0.8223 0.3739 0 0.6883 −0.6028 0 −0.6079 0.3771 0 0.46 −0.6435 0 −0.3936 0.3845 0 0.2298 −0.6755 0 −0.1794 0.3952 0 −0.0011 −0.6982 0 0.0346 0.4086 0 −0.2326 −0.7106 0 0.2484 0.424 0 −0.4648 −0.712 0 0.4622 0.4408 0 −0.6971 −0.7018 0 0.6759 0.4585 0 −0.9285 −0.6795 0 0.8896 0.4764 0 −1.1577 −0.6456 0 1.1033 0.4944 0 −1.3838 −0.6011 0 1.317 0.5123 0 −1.5996 −0.5487 0 1.5236 0.5295 0 −1.8056 −0.4895 0 1.723 0.5457 0 −2.002 −0.4247 0 1.9154 0.5611 0 −2.1892 −0.3556 0 2.1007 0.5756 0 −2.3675 −0.2833 0 2.2789 0.5895 0 −2.5373 −0.2088 0 2.4499 0.6026 0 −2.6982 −0.1334 0 2.6138 0.6151 0 −2.8504 −0.0577 0 2.7635 0.6265 0 −2.9866 0.0153 0 2.8989 0.6368 0 −3.1062 0.0865 0 3.0201 0.646 0 −3.2084 0.1558 0 3.127 0.6542 0 −3.2994 0.2279 0 3.2196 0.6614 0 −3.3716 0.2976 0 3.298 0.6675 0 −3.4203 0.3579 0 3.365 0.6728 0 −3.4521 0.4111 0 3.4213 0.6773 0 −3.4683 0.4546 0 3.4672 0.6741 0 −3.4731 0.4892 0 3.5009 0.6596 0 −3.4718 0.5086 0 3.523 0.6419 0 −3.4689 0.5208 0 3.5365 0.6257 0 −3.467 0.5268 0 3.5456 0.6105 0 −3.466 0.5298 0 3.5513 0.5975 0 3.5515 0.4009 0.5312 −3.4315 0.5931 0.5312 3.5534 0.3897 0.5312 −3.431 0.5945 0.5312 3.554 0.3746 0.5312 −3.4298 0.597 0.5312 3.5515 0.3558 0.5312 −3.4273 0.6022 0.5312 3.544 0.3344 0.5312 −3.4218 0.6122 0.5312 3.5268 0.3097 0.5312 −3.4113 0.6267 0.5312 3.4948 0.2871 0.5312 −3.388 0.6487 0.5312 3.4494 0.2676 0.5312 −3.3512 0.6703 0.5312 3.3942 0.2439 0.5312 −3.2968 0.6866 0.5312 3.3284 0.2159 0.5312 −3.2263 0.6921 0.5312 3.2514 0.1833 0.5312 −3.1345 0.6834 0.5312 3.1602 0.1452 0.5312 −3.03 0.6642 0.5312 3.0548 0.1016 0.5312 −2.9188 0.6424 0.5312 2.9351 0.0529 0.5312 −2.7938 0.6171 0.5312 2.8009 −0.0006 0.5312 −2.6549 0.5895 0.5312 2.6521 −0.0585 0.5312 −2.5019 0.5609 0.5312 2.4886 −0.1204 0.5312 −2.3417 0.5326 0.5312 2.3173 −0.1829 0.5312 −2.1743 0.5049 0.5312 2.1379 −0.2455 0.5312 −1.9997 0.4783 0.5312 1.9504 −0.3077 0.5312 −1.8178 0.4534 0.5312 1.7544 −0.369 0.5312 −1.6285 0.4306 0.5312 1.5501 −0.4283 0.5312 −1.4318 0.4101 0.5312 1.3372 −0.4847 0.5312 −1.2277 0.3923 0.5312 1.1156 −0.5369 0.5312 −1.0161 0.3778 0.5312 0.8924 −0.5825 0.5312 −0.804 0.3674 0.5312 0.6675 −0.6209 0.5312 −0.5915 0.3608 0.5312 0.4415 −0.6514 0.5312 −0.379 0.3579 0.5312 0.2148 −0.6731 0.5312 −0.1664 0.3583 0.5312 −0.0126 −0.6853 0.5312 0.0461 0.3617 0.5312 −0.2409 −0.687 0.5312 0.2586 0.3675 0.5312 −0.469 −0.6776 0.5312 0.471 0.3751 0.5312 −0.6964 −0.6565 0.5312 0.6833 0.3838 0.5312 −0.9223 −0.6238 0.5312 0.8957 0.3931 0.5312 −1.1463 −0.5801 0.5312 1.108 0.4023 0.5312 −1.367 −0.5265 0.5312 1.3204 0.4113 0.5312 −1.5774 −0.4662 0.5312 1.5257 0.4198 0.5312 −1.7778 −0.4005 0.5312 1.7239 0.4274 0.5312 −1.9686 −0.3306 0.5312 1.9151 0.4341 0.5312 −2.1504 −0.2577 0.5312 2.0992 0.4401 0.5312 −2.3234 −0.1828 0.5312 2.2763 0.4454 0.5312 −2.4881 −0.1069 0.5312 2.4462 0.4503 0.5312 −2.6447 −0.0308 0.5312 2.6091 0.4549 0.5312 −2.7933 0.045 0.5312 2.7579 0.459 0.5312 −2.927 0.1166 0.5312 2.8924 0.4627 0.5312 −3.0456 0.184 0.5312 3.0128 0.466 0.5312 −3.1491 0.2474 0.5312 3.1191 0.469 0.5312 −3.2425 0.3121 0.5312 3.2111 0.4717 0.5312 −3.3187 0.3748 0.5312 3.289 0.474 0.5312 −3.3716 0.4292 0.5312 3.3556 0.476 0.5312 −3.4077 0.4778 0.5312 3.4115 0.4778 0.5312 −3.4282 0.5186 0.5312 3.4576 0.479 0.5312 −3.4365 0.5518 0.5312 3.4937 0.4708 0.5312 −3.4368 0.5708 0.5312 3.5182 0.4556 0.5312 −3.4347 0.5829 0.5312 3.5331 0.44 0.5312 −3.4329 0.5888 0.5312 3.5428 0.4247 0.5312 −3.432 0.5917 0.5312 3.5485 0.4114 0.5312 3.5592 0.2261 1.0624 −3.4062 0.6599 1.0624 3.5604 0.215 1.0624 −3.4057 0.6612 1.0624 3.5595 0.2002 1.0624 −3.4045 0.6638 1.0624 3.5547 0.1822 1.0624 −3.402 0.669 1.0624 3.5436 0.1629 1.0624 −3.396 0.6787 1.0624 3.5213 0.1433 1.0624 −3.3844 0.6922 1.0624 3.4852 0.1289 1.0624 −3.3587 0.7111 1.0624 3.4394 0.1125 1.0624 −3.3191 0.7264 1.0624 3.3837 0.0926 1.0624 −3.2631 0.7329 1.0624 3.3174 0.069 1.0624 −3.1926 0.7276 1.0624 3.2397 0.0416 1.0624 −3.1025 0.7105 1.0624 3.1479 0.0094 1.0624 −2.9989 0.6891 1.0624 3.0418 −0.0273 1.0624 −2.8879 0.6684 1.0624 2.9213 −0.0684 1.0624 −2.7632 0.6446 1.0624 2.7865 −0.1136 1.0624 −2.6245 0.6185 1.0624 2.6372 −0.1626 1.0624 −2.4717 0.5911 1.0624 2.4732 −0.2148 1.0624 −2.3118 0.5634 1.0624 2.3017 −0.2675 1.0624 −2.1448 0.5357 1.0624 2.1224 −0.3202 1.0624 −1.9706 0.508 1.0624 1.9351 −0.3725 1.0624 −1.7893 0.4805 1.0624 1.7399 −0.4237 1.0624 −1.6008 0.4537 1.0624 1.5363 −0.4731 1.0624 −1.405 0.4279 1.0624 1.3241 −0.5194 1.0624 −1.2019 0.4035 1.0624 1.1032 −0.5616 1.0624 −0.9914 0.3812 1.0624 0.8814 −0.5972 1.0624 −0.7806 0.3622 1.0624 0.6587 −0.6258 1.0624 −0.5695 0.3464 1.0624 0.4349 −0.6465 1.0624 −0.3582 0.3339 1.0624 0.2104 −0.6586 1.0624 −0.1466 0.3247 1.0624 −0.014 −0.6612 1.0624 0.065 0.3188 1.0624 −0.2383 −0.6532 1.0624 0.2767 0.3158 1.0624 −0.4625 −0.6342 1.0624 0.4884 0.3148 1.0624 −0.685 −0.6039 1.0624 0.7001 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1.317 −0.5402 1.5936 −1.1842 0.416 1.5936 1.096 −0.5719 1.5936 −0.9741 0.3853 1.5936 0.8742 −0.5974 1.5936 −0.7636 0.3571 1.5936 0.6514 −0.6159 1.5936 −0.5528 0.3316 1.5936 0.4284 −0.6269 1.5936 −0.3416 0.3094 1.5936 0.2054 −0.6295 1.5936 −0.1302 0.2908 1.5936 −0.0177 −0.6228 1.5936 0.0815 0.276 1.5936 −0.2406 −0.6055 1.5936 0.2934 0.2646 1.5936 −0.4621 −0.5773 1.5936 0.5056 0.2558 1.5936 −0.6818 −0.5384 1.5936 0.7177 0.2485 1.5936 −0.8996 −0.4889 1.5936 0.93 0.2422 1.5936 −1.1153 −0.4299 1.5936 1.1422 0.2363 1.5936 −1.3283 −0.3629 1.5936 1.3544 0.2304 1.5936 −1.5319 −0.2913 1.5936 1.5596 0.2244 1.5936 −1.7266 −0.2167 1.5936 1.7576 0.2181 1.5936 −1.9127 −0.1401 1.5936 1.9486 0.2113 1.5936 −2.0901 −0.0624 1.5936 2.1324 0.2039 1.5936 −2.2593 0.0154 1.5936 2.3092 0.1961 1.5936 −2.4206 0.0924 1.5936 2.4789 0.1881 1.5936 −2.5744 0.168 1.5936 2.6414 0.18 1.5936 −2.7206 0.2422 1.5936 2.7899 0.1724 1.5936 −2.8527 0.3112 1.5936 2.9241 0.1653 1.5936 −2.971 0.3744 1.5936 3.0443 0.1589 1.5936 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3.2358 −2.2532 14.3421 −3.1483 2.341 14.3421 3.2551 −2.2673 14.3421 −3.1481 2.3473 14.3421 3.2711 −2.279 14.3421 −3.1468 2.3503 14.3421 3.2805 −2.2915 14.3421 3.2891 −2.3916 14.8732 −3.1354 2.4413 14.8732 3.2792 −2.3983 14.8732 −3.1341 2.4423 14.8732 3.2641 −2.3935 14.8732 −3.131 2.4431 14.8732 3.2466 −2.3832 14.8732 −3.1246 2.4424 14.8732 3.2256 −2.3709 14.8732 −3.1129 2.437 14.8732 3.1976 −2.3546 14.8732 −3.0967 2.4251 14.8732 3.1612 −2.3335 14.8732 −3.0694 2.4012 14.8732 3.1156 −2.3072 14.8732 −3.0329 2.3695 14.8732 3.06 −2.2754 14.8732 −2.9838 2.3278 14.8732 2.9938 −2.2377 14.8732 −2.9217 2.2765 14.8732 2.9165 −2.1935 14.8732 −2.8399 2.2112 14.8732 2.8251 −2.1411 14.8732 −2.7441 2.1378 14.8732 2.7195 −2.081 14.8732 −2.6404 2.0612 14.8732 2.5998 −2.0129 14.8732 −2.5224 1.9771 14.8732 2.4667 −1.9356 14.8732 −2.39 1.8854 14.8732 2.3205 −1.8487 14.8732 −2.2434 1.7859 14.8732 2.1614 −1.7519 14.8732 −2.0898 1.6823 14.8732 1.9969 −1.6489 14.8732 −1.9296 1.5743 14.8732 1.8276 −1.5387 14.8732 −1.7628 1.4614 14.8732 1.6539 −1.4209 14.8732 −1.5897 1.3436 14.8732 1.4757 −1.2955 14.8732 −1.4105 1.2205 14.8732 1.2932 −1.1623 14.8732 −1.2252 1.092 14.8732 1.1061 −1.0218 14.8732 −1.0341 0.9578 14.8732 0.9141 −0.8743 14.8732 −0.8373 0.8177 14.8732 0.723 −0.7255 14.8732 −0.6415 0.6762 14.8732 0.5326 −0.5758 14.8732 −0.4468 0.5333 14.8732 0.3424 −0.4259 14.8732 −0.2534 0.3887 14.8732 0.1519 −0.2762 14.8732 −0.0614 0.2423 14.8732 −0.0388 −0.1269 14.8732 0.1293 0.0941 14.8732 −0.2297 0.0221 14.8732 0.3187 −0.0559 14.8732 −0.4206 0.1711 14.8732 0.5067 −0.2076 14.8732 −0.6115 0.3202 14.8732 0.6937 −0.3607 14.8732 −0.8023 0.4693 14.8732 0.88 −0.5145 14.8732 −0.993 0.6186 14.8732 1.0665 −0.6683 14.8732 −1.1837 0.7679 14.8732 1.2535 −0.8212 14.8732 −1.3679 0.9124 14.8732 1.4354 −0.9678 14.8732 −1.5456 1.0521 14.8732 1.6125 −1.1075 14.8732 −1.7166 1.1872 14.8732 1.7847 −1.2403 14.8732 −1.8811 1.3177 14.8732 1.9518 −1.3667 14.8732 −2.0388 1.4436 14.8732 2.1131 −1.4873 14.8732 −2.1898 1.565 14.8732 2.2685 −1.6026 14.8732 −2.3339 1.6821 14.8732 2.4174 −1.7128 14.8732 −2.4709 1.7951 14.8732 2.5532 −1.8138 14.8732 −2.5943 1.8992 14.8732 2.6755 −1.9059 14.8732 −2.7041 1.9944 14.8732 2.7843 −1.9891 14.8732 −2.8004 2.0805 14.8732 2.8803 −2.0625 14.8732 −2.8893 2.1627 14.8732 2.9638 −2.1259 14.8732 −2.9651 2.2353 14.8732 3.0342 −2.1797 14.8732 −3.0227 2.2918 14.8732 3.0943 −2.2258 14.8732 −3.0683 2.3377 14.8732 3.1449 −2.2645 14.8732 −3.102 2.3724 14.8732 3.1865 −2.2962 14.8732 −3.1249 2.4005 14.8732 3.2199 −2.3215 14.8732 −3.1347 2.4181 14.8732 3.2457 −2.341 14.8732 −3.1381 2.4306 14.8732 3.265 −2.3555 14.8732 −3.1377 2.437 14.8732 3.2811 −2.3676 14.8732 −3.1364 2.44 14.8732 3.2911 −2.3798 14.8732 3.2984 −2.4903 15.6492 −3.1156 2.5863 15.6492 3.2881 −2.4966 15.6492 −3.1142 2.5872 15.6492 3.273 −2.4909 15.6492 −3.111 2.588 15.6492 3.2553 −2.4804 15.6492 −3.1045 2.587 15.6492 3.2341 −2.4677 15.6492 −3.0926 2.5811 15.6492 3.2058 −2.4508 15.6492 −3.0766 2.5685 15.6492 3.1691 −2.4288 15.6492 −3.0495 2.5435 15.6492 3.1233 −2.4012 15.6492 −3.0132 2.5103 15.6492 3.0675 −2.3677 15.6492 −2.9644 2.4665 15.6492 3.0011 −2.328 15.6492 −2.9027 2.4126 15.6492 2.9229 −2.2823 15.6492 −2.8213 2.344 15.6492 2.8302 −2.2288 15.6492 −2.7259 2.2667 15.6492 2.7234 −2.1667 15.6492 −2.6225 2.1862 15.6492 2.603 −2.0955 15.6492 −2.5047 2.0976 15.6492 2.4689 −2.015 15.6492 −2.3724 2.0009 15.6492 2.3216 −1.9246 15.6492 −2.2259 1.8959 15.6492 2.1613 −1.824 15.6492 −2.0725 1.7866 15.6492 1.9957 −1.7164 15.6492 −1.9123 1.6724 15.6492 1.8253 −1.6008 15.6492 −1.7457 1.5534 15.6492 1.6508 −1.4768 15.6492 −1.5727 1.4291 15.6492 1.4724 −1.3444 15.6492 −1.3935 1.2994 15.6492 1.2903 −1.2036 15.6492 −1.2083 1.1641 15.6492 1.1041 −1.055 15.6492 −1.0172 1.0228 15.6492 0.913 −0.8992 15.6492 −0.8206 0.8753 15.6492 0.723 −0.7422 15.6492 −0.6252 0.7262 15.6492 0.5334 −0.5846 15.6492 −0.431 0.5754 15.6492 0.3438 −0.427 15.6492 −0.2382 0.4228 15.6492 0.1538 −0.2699 15.6492 −0.047 0.2684 15.6492 −0.0364 −0.1131 15.6492 0.1428 0.1122 15.6492 −0.2268 0.0434 15.6492 0.3312 −0.0458 15.6492 −0.4172 0.2 15.6492 0.5182 −0.2053 15.6492 −0.6075 0.3568 15.6492 0.7041 −0.3662 15.6492 −0.7977 0.5136 15.6492 0.8893 −0.5278 15.6492 −0.9879 0.6705 15.6492 1.0745 −0.6895 15.6492 −1.178 0.8274 15.6492 1.2602 −0.8507 15.6492 −1.3618 0.9791 15.6492 1.4407 −1.0052 15.6492 −1.539 1.1258 15.6492 1.6165 −1.1526 15.6492 −1.7097 1.2676 15.6492 1.7879 −1.2925 15.6492 −1.8736 1.4046 15.6492 1.9544 −1.4255 15.6492 −2.0308 1.5369 15.6492 2.1155 −1.5522 15.6492 −2.1812 1.6646 15.6492 2.2709 −1.673 15.6492 −2.3245 1.7879 15.6492 2.4201 −1.7883 15.6492 −2.4605 1.9071 15.6492 2.5565 −1.8933 15.6492 −2.5828 2.0168 15.6492 2.6797 −1.9886 15.6492 −2.6915 2.1172 15.6492 2.7894 −2.0745 15.6492 −2.7867 2.2079 15.6492 2.8859 −2.1509 15.6492 −2.8745 2.2945 15.6492 2.9692 −2.2173 15.6492 −2.9493 2.3708 15.6492 3.0401 −2.2731 15.6492 −3.006 2.4304 15.6492 3.101 −2.3202 15.6492 −3.0507 2.4786 15.6492 3.1523 −2.3598 15.6492 −3.0838 2.5151 15.6492 3.1945 −2.3923 15.6492 −3.1063 2.5445 15.6492 3.2282 −2.4184 15.6492 −3.1156 2.5627 15.6492 3.2542 −2.4385 15.6492 −3.1187 2.5755 15.6492 3.2736 −2.4536 15.6492 −3.1181 2.582 15.6492 3.2898 −2.4662 15.6492 −3.1167 2.585 15.6492 3.3003 −2.4783 15.6492 3.3002 −2.5052 15.8 −3.1094 2.6142 15.8 3.2898 −2.5115 15.8 −3.108 2.6152 15.8 3.2746 −2.5057 15.8 −3.1047 2.616 15.8 3.2569 −2.495 15.8 −3.0982 2.6149 15.8 3.2357 −2.4822 15.8 −3.0863 2.6089 15.8 3.2073 −2.4652 15.8 −3.0702 2.5962 15.8 3.1705 −2.443 15.8 −3.0432 2.571 15.8 3.1246 −2.4153 15.8 −3.007 2.5374 15.8 3.0687 −2.3816 15.8 −2.9583 2.4932 15.8 3.002 −2.3417 15.8 −2.8966 2.4388 15.8 2.9237 −2.2956 15.8 −2.8153 2.3695 15.8 2.8308 −2.2416 15.8 −2.7201 2.2914 15.8 2.7239 −2.1789 15.8 −2.6169 2.21 15.8 2.6031 −2.1073 15.8 −2.4993 2.1205 15.8 2.4688 −2.0261 15.8 −2.3671 2.0229 15.8 2.321 −1.9353 15.8 −2.2208 1.9168 15.8 2.1603 −1.834 15.8 −2.0675 1.8063 15.8 1.9942 −1.7257 15.8 −1.9075 1.691 15.8 1.8234 −1.6093 15.8 −1.7409 1.5707 15.8 1.6488 −1.4844 15.8 −1.568 1.4452 15.8 1.4704 −1.3511 15.8 −1.389 1.3143 15.8 1.2884 −1.2092 15.8 −1.2039 1.1776 15.8 1.1022 −1.0595 15.8 −1.013 1.0349 15.8 0.9112 −0.9024 15.8 −0.8167 0.8859 15.8 0.7213 −0.7442 15.8 −0.6216 0.7354 15.8 0.5318 −0.5854 15.8 −0.4279 0.5831 15.8 0.3424 −0.4266 15.8 −0.2357 0.429 15.8 0.1526 −0.2682 15.8 −0.0448 0.2731 15.8 −0.0375 −0.1101 15.8 0.1446 0.1154 15.8 −0.2277 0.0478 15.8 0.3327 −0.044 15.8 −0.4178 0.2058 15.8 0.5194 −0.2049 15.8 −0.6077 0.3639 15.8 0.7051 −0.3671 15.8 −0.7976 0.5223 15.8 0.8901 −0.53 15.8 −0.9874 0.6806 15.8 1.0751 −0.693 15.8 −1.1772 0.839 15.8 1.2606 −0.8554 15.8 −1.3605 0.9923 15.8 1.441 −1.0112 15.8 −1.5374 1.1405 15.8 1.6167 −1.1597 15.8 −1.7077 1.2836 15.8 1.7881 −1.3008 15.8 −1.8714 1.4219 15.8 1.9546 −1.4348 15.8 −2.0283 1.5555 15.8 2.1157 −1.5624 15.8 −2.1783 1.6844 15.8 2.2711 −1.684 15.8 −2.3212 1.8089 15.8 2.4204 −1.8 15.8 −2.4569 1.9292 15.8 2.557 −1.9056 15.8 −2.5789 2.04 15.8 2.6804 −2.0014 15.8 −2.6872 2.1413 15.8 2.7903 −2.0877 15.8 −2.7821 2.2328 15.8 2.887 −2.1643 15.8 −2.8696 2.3202 15.8 2.9706 −2.2309 15.8 −2.9441 2.3972 15.8 3.0416 −2.2869 15.8 −3.0005 2.4572 15.8 3.1026 −2.3343 15.8 −3.0451 2.5059 15.8 3.1539 −2.3741 15.8 −3.078 2.5427 15.8 3.1961 −2.4069 15.8 −3.1004 2.5723 15.8 3.2299 −2.4331 15.8 −3.1096 2.5906 15.8 3.2558 −2.4533 15.8 −3.1125 2.6034 15.8 3.2753 −2.4685 15.8 −3.1118 2.61 15.8 3.2915 −2.4812 15.8 −3.1104 2.613 15.8 3.302 −2.4933 15.8 3.3017 −2.5182 15.9356 −3.1028 2.6385 15.9356 3.2912 −2.5245 15.9356 −3.1014 2.6394 15.9356 3.2761 −2.5185 15.9356 −3.0982 2.6402 15.9356 3.2583 −2.5077 15.9356 −3.0916 2.639 15.9356 3.2371 −2.4948 15.9356 −3.0798 2.6331 15.9356 3.2087 −2.4776 15.9356 −3.0637 2.6202 15.9356 3.1718 −2.4553 15.9356 −3.0367 2.5948 15.9356 3.1257 −2.4274 15.9356 −3.0006 2.5611 15.9356 3.0697 −2.3936 15.9356 −2.952 2.5165 15.9356 3.0029 −2.3535 15.9356 −2.8904 2.4617 15.9356 2.9244 −2.307 15.9356 −2.8094 2.3917 15.9356 2.8314 −2.2525 15.9356 −2.7143 2.3129 15.9356 2.7243 −2.1894 15.9356 −2.6114 2.2308 15.9356 2.6032 −2.1172 15.9356 −2.4939 2.1405 15.9356 2.4685 −2.0356 15.9356 −2.3619 2.042 15.9356 2.3204 −1.9442 15.9356 −2.2157 1.9349 15.9356 2.1592 −1.8424 15.9356 −2.0626 1.8234 15.9356 1.9927 −1.7334 15.9356 −1.9028 1.7071 15.9356 1.8217 −1.6163 15.9356 −1.7364 1.5857 15.9356 1.647 −1.4908 15.9356 −1.5637 1.4591 15.9356 1.4686 −1.3567 15.9356 −1.3848 1.327 15.9356 1.2867 −1.214 15.9356 −1.2 1.1891 15.9356 1.1006 −1.0632 15.9356 −1.0093 1.0452 15.9356 0.9098 −0.9052 15.9356 −0.8133 0.8949 15.9356 0.7199 −0.746 15.9356 −0.6185 0.743 15.9356 0.5305 −0.5863 15.9356 −0.4252 0.5893 15.9356 0.3412 −0.4264 15.9356 −0.2332 0.4339 15.9356 0.1516 −0.267 15.9356 −0.0427 0.2767 15.9356 −0.0383 −0.1079 15.9356 0.1464 0.1178 15.9356 −0.2283 0.0511 15.9356 0.3342 −0.0428 15.9356 −0.4182 0.2103 15.9356 0.5207 −0.2049 15.9356 −0.6079 0.3697 15.9356 0.7062 −0.3682 15.9356 −0.7974 0.5292 15.9356 0.891 −0.5322 15.9356 −0.9869 0.6889 15.9356 1.0758 −0.6963 15.9356 −1.1762 0.8487 15.9356 1.2612 −0.8597 15.9356 −1.3592 1.0033 15.9356 1.4415 −1.0165 15.9356 −1.5357 1.1527 15.9356 1.6171 −1.166 15.9356 −1.7056 1.2971 15.9356 1.7884 −1.3079 15.9356 −1.8689 1.4366 15.9356 1.9548 −1.4428 15.9356 −2.0254 1.5713 15.9356 2.1159 −1.5712 15.9356 −2.175 1.7013 15.9356 2.2713 −1.6935 15.9356 −2.3176 1.8268 15.9356 2.4207 −1.8101 15.9356 −2.4529 1.9481 15.9356 2.5574 −1.9162 15.9356 −2.5745 2.0599 15.9356 2.6809 −2.0124 15.9356 −2.6825 2.162 15.9356 2.7911 −2.099 15.9356 −2.7771 2.2543 15.9356 2.8879 −2.1758 15.9356 −2.8643 2.3424 15.9356 2.9717 −2.2425 15.9356 −2.9385 2.42 15.9356 3.0428 −2.2987 15.9356 −2.9947 2.4805 15.9356 3.1039 −2.3464 15.9356 −3.0391 2.5295 15.9356 3.1552 −2.3864 15.9356 −3.0719 2.5666 15.9356 3.1974 −2.4194 15.9356 −3.0941 2.5963 15.9356 3.2311 −2.4458 15.9356 −3.1032 2.6148 15.9356 3.2571 −2.4661 15.9356 −3.1061 2.6277 15.9356 3.2765 −2.4813 15.9356 −3.1054 2.6342 15.9356 3.2928 −2.4941 15.9356 −3.1039 2.6372 15.9356 3.3035 −2.5062 15.9356 3.3141 −2.6189 16.9980 −3.0282 2.7981 16.9980 3.3033 −2.6247 16.9980 −3.0267 2.7990 16.9980 3.2881 −2.6177 16.9980 −3.0234 2.7997 16.9980 3.2704 −2.6063 16.9980 −3.0168 2.7984 16.9980 3.2490 −2.5928 16.9980 −3.0050 2.7922 16.9980 3.2206 −2.5747 16.9980 −2.9889 2.7790 16.9980 3.1834 −2.5514 16.9980 −2.9623 2.7524 16.9980 3.1370 −2.5223 16.9980 −2.9269 2.7169 16.9980 3.0805 −2.4872 16.9980 −2.8794 2.6698 16.9980 3.0131 −2.4454 16.9980 −2.8195 2.6117 16.9980 2.9344 −2.3965 16.9980 −2.7404 2.5372 16.9980 2.8413 −2.3387 16.9980 −2.6475 2.4532 16.9980 2.7337 −2.2723 16.9980 −2.5465 2.3657 16.9980 2.6119 −2.1968 16.9980 −2.4310 2.2695 16.9980 2.4762 −2.1117 16.9980 −2.3009 2.1646 16.9980 2.3269 −2.0166 16.9980 −2.1568 2.0505 16.9980 2.1643 −1.9111 16.9980 −2.0059 1.9314 16.9980 1.9965 −1.7981 16.9980 −1.8487 1.8070 16.9980 1.8246 −1.6768 16.9980 −1.6850 1.6772 16.9980 1.6494 −1.5467 16.9980 −1.5150 1.5419 16.9980 1.4709 −1.4073 16.9980 −1.3389 1.4009 16.9980 1.2893 −1.2588 16.9980 −1.1566 1.2543 16.9980 1.1038 −1.1018 16.9980 −0.9685 1.1016 16.9980 0.9136 −0.9375 16.9980 −0.7749 0.9422 16.9980 0.7242 −0.7722 16.9980 −0.5829 0.7811 16.9980 0.5353 −0.6064 16.9980 −0.3924 0.6183 16.9980 0.3466 −0.4403 16.9980 −0.2032 0.4540 16.9980 0.1579 −0.2743 16.9980 −0.0153 0.2882 16.9980 −0.0309 −0.1083 16.9980 0.1714 0.1211 16.9980 −0.2195 0.0579 16.9980 0.3569 −0.0473 16.9980 −0.4078 0.2244 16.9980 0.5413 −0.2170 16.9980 −0.5958 0.3913 16.9980 0.7247 −0.3877 16.9980 −0.7833 0.5589 16.9980 0.9077 −0.5590 16.9980 −0.9700 0.7272 16.9980 1.0909 −0.7301 16.9980 −1.1560 0.8964 16.9980 1.2749 −0.9001 16.9980 −1.3353 1.0607 16.9980 1.4541 −1.0631 16.9980 −1.5080 1.2196 16.9980 1.6287 −1.2187 16.9980 −1.6743 1.3732 16.9980 1.7989 −1.3666 16.9980 −1.8340 1.5216 16.9980 1.9645 −1.5072 16.9980 −1.9869 1.6649 16.9980 2.1251 −1.6408 16.9980 −2.1328 1.8034 16.9980 2.2803 −1.7679 16.9980 −2.2715 1.9374 16.9980 2.4297 −1.8888 16.9980 −2.4026 2.0671 16.9980 2.5666 −1.9987 16.9980 −2.5201 2.1866 16.9980 2.6905 −2.0980 16.9980 −2.6245 2.2956 16.9980 2.8011 −2.1872 16.9980 −2.7158 2.3939 16.9980 2.8986 −2.2660 16.9980 −2.8002 2.4871 16.9980 2.9832 −2.3341 16.9980 −2.8721 2.5691 16.9980 3.0547 −2.3919 16.9980 −2.9265 2.6328 16.9980 3.1157 −2.4414 16.9980 −2.9694 2.6844 16.9980 3.1669 −2.4831 16.9980 −3.0011 2.7235 16.9980 3.2090 −2.5174 16.9980 −3.0219 2.7549 16.9980 3.2428 −2.5447 16.9980 −3.0300 2.7741 16.9980 3.2688 −2.5658 16.9980 −3.0321 2.7873 16.9980 3.2883 −2.5815 16.9980 −3.0310 2.7939 16.9980 3.3045 −2.5947 16.9980 −3.0293 2.7968 16.9980 3.3157 −2.6068 16.9980

It will also be appreciated that the airfoil 200 disclosed in the above scalable Table 1 may be non-scaled, scaled up or scaled down geometrically for use in other similar turbine/compressor designs. Consequently, the coordinate values set forth in Table 1 may be non-scaled, scaled upwardly or scaled downwardly such that the general airfoil profile shape remains unchanged. A scaled version of the coordinates in Table 1 would be represented by X, Y and Z coordinate values of Table 1, with the X, Y and Z non-dimensional coordinate values converted to inches or mm (or any suitable dimensional system), multiplied or divided by a constant number. The constant number may be a fraction, decimal fraction, integer or mixed number.

The article of manufacture may also have a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1. The Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number. The X and Y coordinates, when connected by smooth continuing arcs, define airfoil profile sections at each Z height. The airfoil profile sections at each Z height are joined smoothly with one another to form a complete suction-side airfoil shape. The X, Y and Z coordinate values being scalable as a function of a number to provide a non-scaled, scaled-up or scaled-down airfoil profile.

The article of manufacture may also have a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1. The Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number. X and Y are coordinates which, when connected by smooth continuing arcs, define airfoil profile sections at each Z height. The airfoil profile sections at each Z height are joined smoothly with one another to form a complete pressure-side airfoil shape. The X, Y and Z values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up and scaled-down airfoil.

The article of manufacture may be an airfoil or a rotor blade configured for use with a compressor. The suction-side airfoil shape may lie in an envelope within +/−5% of a chord length in a direction normal to a suction-side airfoil surface location, or +/−0.25 inches in a direction normal to a suction-side airfoil surface location.

The number, used to convert the non-dimensional values to dimensional distances, may be a fraction, decimal fraction, integer or mixed number. The height of the article of manufacture may be about 1 inch to about 20 inches or more, or any suitable height as desired in the specific application.

A compressor 2, according to an aspect of the present invention, may include a plurality of rotor blades 22. Each of the rotor blades 22 include an airfoil 200 having a suction-side 310 airfoil shape, the airfoil 200 having a nominal profile substantially in accordance with suction-side 310 Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1. The Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number. The number, used to convert the non-dimensional values to dimensional distances, may be a fraction, decimal fraction, integer or mixed number. X and Y are coordinates which, when connected by smooth continuing arcs, define airfoil profile sections at each Z height. The airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side 310 airfoil shape.

The compressor 2, according to an aspect of the present invention, may also have a plurality of rotor blades 22 having a pressure-side 320 nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in scalable Table 1. The Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number. The number (which would be the same number used for the suction side) may be a fraction, decimal fraction, integer or mixed number. X and Y are coordinates which, when connected by smooth continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete pressure-side airfoil shape.

An important term in this disclosure is profile. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in scalable Table 1. The actual profile on a manufactured blade may be different than those in scalable Table 1 and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, an approximately +or −5% chord and/or 0.25 inch profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized.

The following are non-limiting examples of the airfoil profiles embodied by the present invention. On some compressors, each airfoil profile section (e.g., at each Z height) may be connected by substantially smooth continuing arcs. On other compressors, some of the airfoil profile sections may be connected by substantially smooth continuing arcs. Embodiments of the present invention may also be employed by a compressor having stage(s) with no airfoil profile sections connected by substantially smooth continuing arcs.

The disclosed airfoil shape increases reliability and is specific to the machine conditions and specifications. The airfoil shape provides a unique profile to achieve (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade or vane loadings. The disclosed loci of points allow the gas turbine and compressor or any other suitable turbine/compressor to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil may be adopted as long as (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled compressor.

The airfoil 200 described herein thus improves overall compressor 2 efficiency. Specifically, the airfoil 200 provides the desired turbine/compressor efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 200 also meets all aeromechanics, loading and stress requirements.

It should be understood that the finished article of manufacture, blade or vane does not necessarily include all the sections defined in the one or more tables listed above. The portion of the airfoil proximal to a platform (or dovetail) and/or tip may not be defined by an airfoil profile section. It should be considered that the airfoil proximal to the platform or tip may vary due to several imposed constraints. The airfoil contains a main profile section that is substantially defined between the inner and outer flowpath walls. The remaining sections of the airfoil may be partly, at least partly or completely located outside of the flowpath. At least some of these remaining sections may be employed to improve the curve fitting of the airfoil at its radially inner or outer portions. The skilled reader will appreciate that a suitable fillet radius may be applied between the platform and the airfoil portion of the article of manufacture, blade or vane.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

The invention claimed is:
 1. An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.
 2. The article of manufacture according to claim 1, wherein the article of manufacture comprises an airfoil configured for use with a compressor.
 3. The article of manufacture according to claim 1, wherein the article of manufacture comprises a rotor blade configured for use with a compressor.
 4. The article of manufacture according to claim 1, wherein the airfoil shape lies in an envelope within one of: +/−5% of a chord length in a direction normal to an airfoil surface location; and +/−0.25 inches in a direction normal to an airfoil surface location.
 5. The article of manufacture according to claim 1, wherein the number, used to convert the non-dimensional values to dimensional distances, is one of a fraction, decimal fraction, integer and mixed number.
 6. The article of manufacture according to claim 1, wherein a height of the article of manufacture is about 1 inch to about 20 inches.
 7. An article of manufacture having a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape, the X, Y and Z coordinate values being scalable as a function of the number to provide one of a non-scaled, scaled-up and scaled-down airfoil profile.
 8. The article of manufacture according to claim 7, wherein the article of manufacture comprises an airfoil configured for use within a compressor.
 9. The article of manufacture according to claim 7, wherein the article of manufacture comprises a rotor blade configured for use with a compressor.
 10. The article of manufacture according to claim 7, wherein the suction-side airfoil shape lies in an envelope within one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location; and +/−0.25 inches in a direction normal to a suction-side airfoil surface location.
 11. The article of manufacture according to claim 7, wherein the number, used to convert the non-dimensional values to dimensional distances, is one of a fraction, decimal fraction, integer and mixed number.
 12. The article of manufacture according to claim 7, wherein a height of the article of manufacture is about 1 inch to about 20 inches.
 13. The article of manufacture according to claim 7, further comprising the article of manufacture having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete pressure-side airfoil shape, the X, Y and Z values being scalable as a function of the number to provide one of a non-scaled, scaled-up and scaled-down airfoil.
 14. A compressor comprising a plurality of rotor blades, each of the rotor blades including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by the number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape.
 15. The compressor according to claim 14, wherein the suction-side airfoil shape lies in an envelope within one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location; and +/−0.25 inches in a direction normal to a suction-side airfoil surface location.
 16. The compressor according to claim 14, wherein the number, used to convert the non-dimensional values to dimensional distances, is one of a fraction, decimal fraction, integer and mixed number.
 17. The compressor according to claim 14, wherein a height of each rotor blade is about 1 inch to about 20 inches.
 18. The compressor according to claim 14, further comprising each of the plurality of rotor blades having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by the number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete pressure-side airfoil shape.
 19. The compressor according to claim 18, wherein the pressure-side airfoil shape lies in an envelope within one of: +/−5% of a chord length in a direction normal to a pressure-side airfoil surface location; and +/−0.25 inches in a direction normal to a pressure-side airfoil surface location.
 20. The compressor according to claim 18, wherein the number, used to convert the non-dimensional values to dimensional distances, is one of a fraction, decimal fraction, integer and mixed number. 